# How to Convert Annual Interest Rate to Daily Interest Rate

Annual interest rates allow you to quickly compare how much interest you'll earn or pay on different types of accounts. However, the annual rates aren't particularly useful for figuring out how much money your deposit account is making or how much interest your loans are accruing on a daily basis. That's where daily interest rates come in. Knowing how to convert from an annual interest rate to a daily interest rate helps you budget for the short term.

## Simple Interest Versus Compound Interest

Simple interest refers to interest calculated without considering interest compounding. For example, if interest is added to your account once per year, and you want to find out how much interest each day adds, you can calculate the daily interest rate using the simple interest formula.

Compound interest, on the other hand, accounts for the additional interest that is generated by interest added to your account throughout the year. For example, if interest compounds daily during the course of the year, the interest that is added after the first day then earns additional interest for the rest of the year.

## Simple Interest Formula

To convert your annual interest rate to a daily interest rate based on simple interest, divide the annual interest rate by 365, the number of days in a year. For example, say your car loan charges 14.60 percent simple interest per year. Divide 14.60 percent by 365 to find the daily interest rate equals 0.04 percent. So, if your loan balance is \$8,000, you would be paying \$3.20 in interest each day.

## Compound Interest Formula

To convert your annual interest rate to a daily interest rate based on compound interest, the formula is more complicated and involves using exponents. For example, if a certificate of deposit (CD) offers you an annual percentage yield (APY) of 4.1 percent and compounds interest daily, you can use the following formula to find the daily interest rate. First, divide the APY by 100 to convert to a decimal. Second, add 1. Third, raise the result to the 1/365th power. Fourth, subtract 1. Fifth, multiply by 100 to find the daily interest rate.

For the example above using the APY of 4.1 percent, you would divide 4.1 by 100 to get 0.041. Second, add 1 to get 1.041. Third, raise 1.041 to the 1/365th power (using a calculator, look for the "^" key or "x^y" key) to get 1.0011. Fourth, subtract 1 to get 0.0011. Fifth, multiply by 100 to find the daily interest rate is 0.11 percent. Therefore, if your CD balance was \$1,000, you would earn 11 cents of interest that day.